Hi, unfortunately some of the previous responses here are not completely correct.
1. Compass accuracy in the northern and southern hemispheres
Steve is right. A typical compass optimized to the northern hemisphere will be less accurate in the southern hemisphere. I know this may seem surprising to some.
The reason is
magnetic dip (inclination). Magnetic lines run nearly parallel to the earth's surface near the equator, but curve downwards near the poles. So, the north-end of a magnetic compass needle will want to point "downwards" in the northern hemisphere, but will want to point "upwards" in the southern hemisphere.
This dip angle may cause the compass needle to "drag" within the compass housing, compromising its accuracy. The compass needle must freely "float" within the compass housing for it to work well.
Hence precision compass needles are actually balanced to work in specific regions. In the northern hemisphere, compass needles are made slightly longer or heavier on their "south" end to counter this tendency for the "north" end to "dip down".
Some manufacturers produce up to five different versions of each compass optimized for various regions of the world.
Other designs allow the needle to freely float even at high dip angles, usually by having another mechanical axis to allow the needle to level itself within a deep housing. Often the needle is actually a free-floating "ball". Marine and aviation compasses tend work this way.
Suunto Global is an example of a field compass designed to work well anywhere. Compare that to the
Suunto Clipper, which must be balanced for either the northern or southern hemisphere.
2. Electronic compass in GPS receivers
There are two different kinds of azimuth information to consider.
When you are moving, virtually any GPS receiver can calculate your
heading based on your ground track in relation to the satellites. You must be moving and have adequate satellite lock for the heading to be accurate. As soon as you stop, the heading becomes unreliable.
Many (but not all) GPS receivers also have a built-in electronic compass. An electronic compass determines
cardinal direction based on the local magnetic field, much like a physical compass. An electronic compass still work even when you're not moving, and does not depend on any satellites. Most electronic compass designs require the unit to be held at a specific angle, unless it has tilt-compensation built-in.
Neither type above are subject to "magnetic dip" because with an electronic compass there is no physical needle to "drag" on the compass housing. Therefore electronic compasses work equally well in any hemisphere, and even when located very close to the poles.
3. Magnetic Declination vs Deviation
Magnetic Declination (not Deviation, see below) is the difference between magnetic north and true north. Many charts show the amount of declination in different sections of the chart, which can be considerable. Aeronautical charts used by pilots, for example, have
isogonic lines showing areas of equal magnetic declination (also called magnetic variation).
Magnetic Deviation is the error to the compass caused by nearby metals / magnetic fields. For example, a nearby electric motor can deviate a compass from its true reading. In fact, the compass housing / mount itself might deflect the compass needle. A compass
correction card are often mandated for critical applications (such as in aircraft, etc.)
Probably more than you'd like to know about compasses.